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The error begins in line zero: Calculate without fixing a definition of $e^z$.
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Martin BrandenburgMar 17 '12 at 15:09

3

That is not the problem, $e^z=1+z+{1\over 2}z^2 +{1\over 6}z^3+\ldots$ is perfectly well-defined.
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Robert KucharczykMar 17 '12 at 15:11

2

The problem is not with defining $e^z$. It's with defining $a^z$ for $a\neq e$.
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Steven LandsburgMar 17 '12 at 15:26